Communications in Statistics: Theory and Methods

Abeidallah, M.; Mechab, B.; Merouan, T.

doi: 10.1080/03610926.2019.1580735pmid: N/A

AbstractThe purpose of the present paper is to investigate by the local linear method a nonparametric estimator of the point at high risk of scalar response variable given a functional variable when the observations are spatially dependent. The main goal is to establish the almost complete convergence with rate of this estimator under some general conditions. A practical example on the climatological data shows the usefulness of our theoretical study.

Khattree, Ravindra

doi: 10.1080/03610926.2019.1576895pmid: N/A

AbstractConstant block-sum designs are of interest in repeated measures experimentation where the treatments levels are quantitative and it is desired that at the end of the experiments, all units have been exposed to the same constant cumulative dose. It has been earlier shown that the constant block-sum balanced incomplete block designs do not exist. As the next choice, we, in this article, explore and construct several constant block-sum partially balanced incomplete block designs. A natural choice is to first explore these designs via magic squares and Parshvanath yantram is found to be especially useful in generating designs for block size 4. Using other techniques such as pair-sums and, circular and radial arrangements, we generate a large number of constant block-sum partially balanced incomplete block designs. Their relationship with mixture designs is explored. Finally, we explore the optimization issues when constant block-sum may not be possible for the class of designs with a given set of parameters.

Li, Na; Liu, Xuhua

doi: 10.1080/03610926.2019.1576896pmid: N/A

AbstractThis paper focuses on inference based on the confidence distributions of the nonparametric regression function and its derivatives, in which dependent inferences are combined by obtaining information about their dependency structure. We first give a motivating example in production operation system to illustrate the necessity of the problems studied in this paper in practical applications. A goodness-of-fit test for polynomial regression model is proposed on the basis of the idea of combined confidence distribution inference, which is the Fisher’s combination statistic in some cases. On the basis of this testing results, a combined estimator for the p-order derivative of nonparametric regression function is provided as well as its large sample size properties. Consequently, the performances of the proposed test and estimation method are illustrated by three specific examples. Finally, the motivating example is analyzed in detail. The simulated and real data examples illustrate the good performance and practicability of the proposed methods based on confidence distribution.

Hu, Sigui; Wang, Honglei

doi: 10.1080/03610926.2019.1576897pmid: N/A

AbstractIn order to save more test cost, assurance test and its equivalent truncated sequential test are studied. In a commonly used case, the operating characteristic (OC) function and expected test time (ETT) function of an assurance test are derived in a concise way. Equivalent test and relative concepts are defined. The procedures to construct a near equivalent truncated sequential test of an assurance test are established. Computation studies show that the near equivalent truncated sequential tests proposed in this paper keep almost the same OC curves with the assurance tests respectively. However, they can save the ETTs dramatically. In fact, the results show that the near equivalent truncated sequential tests can save around 50% of ETTs than the assurance tests respectively.

Sanaullah, Aamir; Saleem, Iram; Shabbir, Javid

doi: 10.1080/03610926.2019.1576898pmid: N/A

AbstractIn this article, we propose new efficient and more generalized difference-cum-exponential type estimator and generalized-difference-cum-generalized exponential type estimators for estimating the mean of sensitivity variable using the auxiliary information. We also discuss theoretically that proposed generalized estimators are more efficient than Sousa et al. (2010), Gupta et al. (2012) and Koyuncu, Gupta, and Sousa (2014) estimators. Results from a real life application and simulation study are presented to demonstrate the performance of the proposed mean estimators in relation to some of the existing mean estimators.

Lin, Jianxi

doi: 10.1080/03610926.2019.1576900pmid: N/A

AbstractIn this paper the second order asymptotics of the tail probabilities of randomly weighted sums and their maxima are established in the case that the underlying primary random variables are subexponential. No any assumption is made on the dependence structure between the random weights, but we assume these weights are bounded away from zero and infinity.

Hu, Guozhi; Cheng, Weihu; Zeng, Jie

doi: 10.1080/03610926.2019.1580736pmid: N/A

AbstractThis paper is concerned with model averaging procedure for varying-coefficient partially linear models. We proposed a jackknife model averaging method that involves minimizing a leave-one-out cross-validation criterion, and developed a computational shortcut to optimize the cross-validation criterion for weight choice. The resulting model average estimator is shown to be asymptotically optimal in terms of achieving the smallest possible squared error. The simulation studies have provided evidence of the superiority of the proposed procedures. Our approach is further applied to a real data.

Li, Yongming; Zhou, Yong

doi: 10.1080/03610926.2019.1580737pmid: N/A

AbstractIn this paper, the survival function and hazard rate estimator by the Kaplan–Meier method are considered, where the survival times and censoring times are two sequences of extended negatively dependent. Under some suitable conditions, the uniform strong approximation rates for the survival function and hazard rate estimator are established with the rate a.s., also, their strong representations are obtained with a remainder a.s. Our results generalize and extend the corresponding ones in the related literatures.

Bickel, David R.

doi: 10.1080/03610926.2019.1580739pmid: N/A

AbstractConfidence sets, p values, maximum likelihood estimates, and other results of non-Bayesian statistical methods may be adjusted to favor sampling distributions that are simple compared to others in the parametric family. The adjustments are derived from a prior likelihood function previously used to adjust posterior distributions.

Kerns, Lucy

doi: 10.1080/03610926.2019.1580740pmid: N/A

AbstractIn risk assessment, it is often desired to make inferences on the minimum dose levels (benchmark doses or BMDs) at which a specific benchmark risk (BMR) is attained. The estimation and inferences of BMDs are well understood in the case of an adverse response to a single-exposure agent. However, the theory of finding BMDs and making inferences on the BMDs is much less developed for cases where the adverse effect of two hazardous agents is studied simultaneously. Deutsch and Piegorsch [2012. Benchmark dose profiles for joint-action quantal data in quantitative risk assessment. Biometrics 68(4):1313–22] proposed a benchmark modeling paradigm in dual exposure setting—adapted from the single-exposure setting—and developed a strategy for conducting full benchmark analysis with joint-action quantal data, and they further extended the proposed benchmark paradigm to continuous response outcomes [Deutsch, R. C., and W. W. Piegorsch. 2013. Benchmark dose profiles for joint-action continuous data in quantitative risk assessment. Biometrical Journal 55(5):741–54]. In their 2012 article, Deutsch and Piegorsch worked exclusively with the complementary log link for modeling the risk with quantal data. The focus of the current paper is on the logit link; particularly, we consider an Abbott-adjusted [A method of computing the effectiveness of an insecticide. Journal of Economic Entomology 18(2):265–7] log-logistic model for the analysis of quantal data with nonzero background response. We discuss the estimation of the benchmark profile (BMP)—a collection of benchmark points which induce the prespecified BMR—and propose different methods for building benchmark inferences in studies involving two hazardous agents. We perform Monte Carlo simulation studies to evaluate the characteristics of the confidence limits. An example is given to illustrate the use of the proposed methods.